Run Expectancy in Baseball, Explained

A run expectancy matrix holds the average runs a team went on to score from each of twenty-four base-out states. It is the number behind every modern claim about whether a decision was worth taking — and this page reproduces none of it, for two reasons it sets out rather than hides.

What a run expectancy matrix is, and what varies

The arithmetic a pair of values supports, and where it is done

What this page will do with run expectancy, and what it refuses to

Twenty-four numbers, one matrix per park per season, and a licence this author did not read

Run expectancy is the simplest idea in modern baseball analysis and the hardest one for a page like this to serve. Take a moment in an inning — a runner on second, one out — and ask how many runs teams in that exact position have gone on to score before the inning ended. FanGraphs defines it as what “provides the average number of expected runs per inning given the current number of outs and placement of baserunners”. There are eight ways the bases can be occupied and three out states, so there are twenty-four such numbers, and together they are a run expectancy matrix. Nearly every modern claim that a decision was or was not worth taking is a subtraction between two cells of one.

A run expectancy matrix is twenty-four numbers: eight arrangements of baserunners against three out states, each holding the average runs a team went on to score from that position in the inning. There is not one matrix. FanGraphs, which publishes the clearest public explanation of it, says the matrices are “unique ones for each park and year based on run scoring”, and the example in its own glossary is described as “roughly neutral for 2014” at 4.15 runs a game. The footer of that same site records its Run Expectancy data as “licenced from TangoTiger.com”. This site therefore reproduces no value from any run expectancy matrix: a licence demonstrably exists and its terms were not read, this engine has no table lookup of any kind, and a fitted stand-in would be wrong at precisely the base-out states a decision turns on.

There are two separate obstacles here and either on its own would be enough. The first is this engine. The expression language behind every calculator on this site is numeric only — no strings, no arrays, no table lookup of any kind — so a reference table has to be either a static block of text on the page or a chain of conditions over a dropdown. Twenty-four values that are recomputed for every park in every season are neither, and a fitted stand-in is worse than nothing: a smooth curve through twenty-four points is worst in the corners, and bases loaded with nobody out and bases empty with two out are exactly the states where a decision is close. The second obstacle is ownership. FanGraphs displays a matrix in its glossary and the footer of that same site records its Run Expectancy data as licensed from TangoTiger.com. This author did not read that licence, so the finding recorded here is the weaker one available — a licence exists and its terms are unknown — and the response is the same either way: no value from any matrix appears anywhere on this site. One further sourcing note, for completeness: Baseball-Reference’s own page on run and win expectancy could not be read at all, because the fetcher refused it with a permission error, so no definition of run expectancy from that site is quoted here.

What can be done without the table is more than it sounds. A run VALUE is just a difference between two of those twenty-four numbers, and the arithmetic on top of it is short. FanGraphs’ measured +0.169 runs for a stolen base and −0.394 for a caught stealing are averages of exactly that subtraction across many attempts. Set the expected change to zero and the break-even success rate falls out as the cost divided by the sum of the cost and the gain. DRaysBay writes the algebra out in one line — “solving for x where x is our runners chance of making it safely to third” — and gets 71% for a runner on second with one out tagging up. So this site does the division and takes the two values from the reader, with published defaults, on the stolen base success and break-even calculator. That is the same pattern athletics’ age-graded performance page uses for its own published factor tables, which it takes from the reader for the no-interpolation reason above and makes no licence claim about: do the arithmetic honestly against a number the reader can look up, rather than guess at the table.

How much a break-even moves between states is itself the argument for this page. The same DRaysBay author who worked the tag-up cleanly then tried to produce a stolen-base break-even from the same 2014 table, got a figure around 60% that he knew was too low, then got a negative one, and published the attempt instead of an answer. That is more useful than a number would have been: it shows that a league-average break-even and a break-even for one runner on one base with one number of outs are different quantities, and that the second needs values this site does not hold. FanGraphs’ own measured figure carries the same warning in gentler words — “There are stolen base attempts with a breakeven well below 70%, and ones with a breakeven above it.”

This is the fifth refusal page in this section, and it is not quite like the other four. The WAR explainer computes nothing because neither publisher of wins above replacement discloses a complete specification and both use proprietary fitted defensive models. Total QBR is withheld in the same way, expected goals is not one formula at all because every provider fits its own, and the Duckworth-Lewis-Stern method keeps its resource tables closed. Run expectancy is the opposite case and worth separating from them: the method is fully public, there is no model and nothing is estimated, and anybody with a season’s play-by-play record could compute the matrix themselves. What stands in the way here is one table’s ownership and one engine’s limits, not secrecy. That is a better position for a reader to be in, because it means the numbers can be looked up and used rather than merely explained.

So what should you actually do. Find a matrix that names its park and its season, take the two values your question needs, and bring them to the stolen-base page, which will do the division and show you the margin. If the decision you are weighing is not a steal, the same two subtractions and one division apply unchanged. And if you want the player-level figure built on the whole matrix — RE24 — that belongs to the publishers who hold the data, which is also the answer the WAR explainer gives for its own subject. The baseball figures this site does compute exactly, from a published box score and a rule number, are the earned run average, the batting percentages and the extra-base decomposition.

Frequently asked questions

Related calculators

References

1. FanGraphs Library. RE24 — defines RE24 as “run expectancy based on the 24 base-out states” and run expectancy as what “provides the average number of expected runs per inning given the current number of outs and placement of baserunners”. It states that the matrices are “unique ones for each park and year based on run scoring” and that RE24 uses “the run expectancy matrix for the given park in a particular year”; its displayed example is described as “roughly neutral for 2014” at 4.15 runs a game, and a win is worth “between 9 and 10 runs depending on the year”. A full 24-state matrix DID come through as real text rather than as an image. NO VALUE FROM IT IS REPRODUCED ON THIS SITE: the footer of the same site records its Run Expectancy data as licensed from TangoTiger.com, and that licence was not read. library.fangraphs.com (read 15 Oct 2026).
2. “Breaking Even Is for Suckers.” FanGraphs, blogs.fangraphs.com — measures the average run value of a successful steal at +0.169 runs and of a caught stealing at -0.394, and concludes “Do the math, and that means that a 70% success rate has zero expected value. Exclude double steals from the analysis, and it’s about 71%.” It is explicit that this is a league-wide average and not a per-attempt figure — “There are stolen base attempts with a breakeven well below 70%, and ones with a breakeven above it” — and that “Maybe the breakeven rate is a bit different than my estimate.” The run values come from the site’s own play-by-play database; the FOOTER of the same site records its Run Expectancy data as “licenced from TangoTiger.com”, with play-by-play credited to Sports Info Solutions and Retrosheet (read 15 Oct 2026).
3. “Calculating baserunning break even points.” DRaysBay, 9 August 2020 — sets out the algebra this site reproduces: “Let’s do algebra, solving for x where x is our runners chance of making it safely to third”, worked as “.221*x – .549*(1-x) = 0” to give 71% for a runner on second with one out tagging up to third. Its run expectancy values are taken from “the RE24 table published in the FanGraphs glossary from 2014”, so it is NOT an independent source for those numbers. Recorded here because the author attempted a stolen-base break-even from the same table, got a figure he knew was too low and then a negative one, and published the failure — which is the clearest available evidence that a break-even depends on the exact base-out state and not on a league average. Its tables came through as text, not images (read 15 Oct 2026).
4. FanGraphs Library. wSB — “wSB = (SB * runSB) + (CS * runCS) – (lgwSB * (1B + BB + HBP – IBB))”, where “the run value of a stolen base is set at .2 runs for all seasons” and “runCS = – (2 x RunsPerOut + 0.075)”, which “changes from year to year to reflect the changing value of runs and outs over the season”. Its own rule of thumb is that “you want to have at least twice as many SB as CS to break even”, which is 66.7% and not the 70% its own blog derives; the page attributes the rule of thumb to nobody and says only that it “bounces around based on the run environment”. library.fangraphs.com (read 15 Oct 2026).
5. Major League Baseball. Glossary: Stolen-base Percentage (SB%) — “Stolen-base percentage is determined by the number of steals for a player divided by his total number of attempts.” Its rule of thumb is that “an SB% of 75 or higher is typically helping his team”, and it states qualitatively that “a caught stealing is much more harmful than a stolen base is helpful” while giving no run values, no break-even figure and no rule number. mlb.com (read 15 Oct 2026).